Problem: Simplify the following expression: $ t = \dfrac{6q + 8}{q + 8} + \dfrac{8}{5} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{6q + 8}{q + 8} \times \dfrac{5}{5} = \dfrac{30q + 40}{5q + 40} $ Multiply the second expression by $\dfrac{q + 8}{q + 8}$ $ \dfrac{8}{5} \times \dfrac{q + 8}{q + 8} = \dfrac{8q + 64}{5q + 40} $ Therefore $ t = \dfrac{30q + 40}{5q + 40} + \dfrac{8q + 64}{5q + 40} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{30q + 40 + 8q + 64}{5q + 40} $ $t = \dfrac{38q + 104}{5q + 40}$